1. Technical Field
The invention relates to a color processing technique for converting a target M-dimensional color signal in an input color space into an N-dimensional output color signal (N>M) in an output color space.
2. Related Art
To express colors by a color output device, inputted color signals (input color signals) need to be converted into coloring materials (output color signals) included in the color output device. Input color signals are often color signals called colorimetric color signals such as L*a*b* and XYZ or standardized color signals such as sRGB and sYCbCr. In most cases, output color signals contain primary colorants such as C (cyan), M (magenta) and Y (yellow), and extra colorants such as K (black) In such cases, input color signals must be converted into output color signals with a larger number of dimensions.
Generally, to convert input color signals into output color signals with a larger number of dimensions, the number of unknown quantities of the output color signals needs to be matched with the number of known quantities of the input color signals. For example, to convert an input color signal of L*a*b* (hereinafter L*a*b* will be described as an example) into an output color signal of CMYK, any one of CMYK needs to be decided in advance. In this case, there is often used a method for deciding CMY on the basis of L*a*b* and K after deciding K on the basis of L*a*b* to reduce the number of unknown quantities from 4 to 3.
To decide CMY on the basis of L*a*b* and K, a color conversion model for converting CMYK into L*a*b* can be used. As the color conversion model, a color conversion model called “black box model” or a color conversion model called “physical model” is used. In the black box model, unknown colors are decided statistically on the basis of pairs of data CMYK and L*a*b* as calorimetric values of CMYK. Examples of the black box model are color transmission characteristic prediction methods described in JP Hei. 10-262157 A (corresponding to U.S. Pat. No. 6,100,999) and JP 2002-84434 A, and known scientific methods using neural networks. In the physical model, unknown colors are calculated on the basis of overlapping of coloring materials. Examples of the physical model are known scientific techniques such as a Neugebauer physical model.
When the model is F, an expression for converting CMYK into L*a*b* is given as follows.(L*,a*,b*)=F(C,M,Y,K)  (Expression 1)
When inversion of the model is F−1, conversion of L*a*b* into CMYK can be given as follows.(C,M,Y)=F−1(L*,a*,b*,K)  (Expression 2)
On this occasion, a method for deciding K is important. In most cases, K is expressed in a function of L*a*b* as follows.K=f(L*,a*,b*)  (Expression 3)
For use of the expression 3, it is necessary to calculate a maximum value of K (=Kmax) enough to reproduce a color of L*a*b* and a minimum value of K (=Kmin) necessary to reproduce the same color of L*a*b*. For example, Kmax and Kmin can be obtained by searching a range of 0≦K≦100. Moreover, K to be used may be controlled in a range of Kmin≦K≦Kmax by a function fK in accordance with input L*a*b*. For example, parameters of the function fK in use of the expression 3 can be decided in accordance with the setting of image quality in such a manner that K is brought close to Kmin when a*b* is large (i.e. chromaticness is high) and K is brought close to Kmax when a*b* is small (i.e. chromaticness is low).
An example of conversion of L*a*b* into CMYK in the case where a color signal of L*a*b* is input to a color output device and a color signal of CMYK is output from the color output device has been described above. An example of separation into coloring materials CMYKRGB in the case where the output color signal contains extra colorants R (red), G (green) and B (blue) in addition to the primary colorants CMY and the extra colorant K will be described below.
When the output color signal of the color output device includes extra colorants K (black), R (red), G (green) and B (blue) for extending a color gamut allowed to be reproduced by the device, in addition to the primary colorants C (cyan), M (magenta) and Y (yellow), a problem in conversion cannot be solved by decision of K. The problem is not simple. Various techniques from an easy technique to a complex technique have been proposed for deciding extra colorants KRGB.
The technique described in U.S. Pat. No. 4,812,899 is a technique generally called “Kueppers Technique”. This technique converts RGB into CMYKRGB by replacing RGB components with CMYK components in accordance with the degree of overlapping of components of an input color signal when the input color signal is an RGB signal obtained from a scanner with respect to a color output device which outputs a color signal including colorants CMYKRGB. Although this technique is so simple that it is easy to put this technique into practice, the color gamut of the output device cannot be used sufficiently and calorimetric color matching can hardly be made.
When the technique is applied to the case where the input color signal is L*a*b*, CMY may be separated into KRGB in accordance with the degree of overlapping of CMY calculated after L*a*b* is converted into CMY (uniquely decided because of conversion of three dimensions into three dimensions). The problem in insufficient use of the color gamut and difficulty of calorimetric color matching however occurs in this case like the case where the input color signal is RGB.
On the other hand, JP Hei. 2001-136401 A has described a technique called “dividing method”. When, for example, the color gamut of the output device is expressed in CMYKRGB, the color gamut is divided into color gamuts each expressed in four colorants, such as a color gamut expressed in YMCK, a color gamut expressed in YMRK, etc. Models are applied to the split color gamuts respectively as follows.
The case where a color gamut expressed in YMCKR is divided and modeled will be described as an example. First, a YMCK color gamut can be given by the expression:(Y,M,C)=FYMCK−1(L*,a*,b*,K)  (Expression 5)in accordance with the expression:(L*,a*,b*)=FYMCK(Y,M,C,K)  (Expression 4)in which FYMCK is a color conversion model for the YMCK color gamut. Similarly, a YMRK color gamut can be given by the expression:(Y,M,R)=FYMRK−1(L*,a*,b*,K)  (Expression 7)in accordance with the expression:(L*,a*,b*)=FYMRK(Y,M,R,K)  (Expression 6)in which FYMRK is a color conversion model for the YMRK color gamut.
In the case of G or B, the color gamut can be divided and modeled in the same manner as the expressions 6 and 7.
The dividing method warrants calorimetric reproducibility in the split color gamuts. Moreover, the split color gamuts can be used sufficiently. It is however difficult to warrant color continuity in a boundary between the YMCK color gamut and the YMRK color gamut because models are selected in accordance with the values of L*a*b*. For this reason, there is a great deal of possibility that a pseudo surface will be generated in an image when a table of color conversion of L*a*b into CMYKRGB is generated by the aforementioned method and applied to an output device. As measures to solve this problem, a technique for smoothing the color conversion table has been described in JP 2001-136401 A. Although color continuity can be improved by smoothing, calorimetric reproducibility is lowered.
As described above, in the dividing method described in JP 2001-136401 A, it is difficult to balance color continuity with calorimetric reproducibility.
As another technique, a method for extending a CMYK system given by the expressions 1 to 3 has been described, for example, in JP 2005-176280 A. An exemplary embodiment of this technique has been described in the case of a six color system of CMYKRG as an example. Conversion of CMYKRG into L*a*b* is given by the expression:(L*,a*,b*)=F(C,M,Y,K,R,G)  (Expression 8)in which F is a model given for the CMYKRG system in the same manner as in the expression 1.
When the expression 2 is extended, inversion of the expression 8 can be given as follows.(C,M,Y)=F−1(L*,a*,b*,K,R,G)  (Expression 9)
A technique for generating KRG is further required because it is necessary to decide KRG before inversion is performed by the expression 9. Therefore, a maximum value of K (=Kmax) enough to reproduce L*a*b* and a minimum value of K (=Kmin) necessary to reproduce L*a*b* must be calculated by retrieval in the same manner as in the case of the CMYK system, and values of Rmax, Rmin, Gmax and Gmin must be retrieved likewise. Because these values are not uniquely decided with respect to L*a*b* so that the values of Rmax, Rmin, Gmax and Gmin vary in accordance with the value of K even in the same L*a*b*, a complex process is required.
Therefore, in JP 2005-176280 A, RG are fixed (R=0, G=0) and only retrieval of Kmax and Kmin from L*a*b* is performed first. The values of Kmax and Kmin calculated thus and K activity αK are used for deciding K as follows.K=αK·Kmax+(1−αK)Kmin  (Expression 10)
Then, K calculated by the expression 10 is fixed and a maximum value Rmax of R enough to reproduce L*a*b* and a minimum value Rmin of R necessary to reproduce L*a*b* are retrieved. After Rmax and Rmin are calculated, R activity αR is used for deciding R as follows in the same manner as the expression 10.R=αR·Rmax+(1−αR)Rmin  (Expression 11)
Finally, K and R calculated by the expressions 10 and 11 are fixed and a maximum value Gmax of G enough to reproduce L*a*b* and a minimum value Gmin of G necessary to reproduce L*a*b* are retrieved. After Gmax and Gmin are calculated, G activity αG is used for deciding G as follows in the same manner as the expression 10 or 11.G=αG·Gmax+(1−αG)Gmin  (Expression 12)
When KRG calculated thus and L*a*b* are applied to the expression 9, CMY can be calculated. K activity αK, R activity αR and G activity αG in the expressions 10, 11 and 12 can be changed in accordance with the values of L*a*b* as follows.αK=UK(L*,a*,b*)  (Expression 13)αR=UR(L*,a*,b*)  (Expression 14)αG=UG(L*,a*,b*)  (Expression 15)
When, for example, UK in the expression 13 is a function for outputting a value which increases as a*b* decreases, K can be used frequently for a color of low chromaticness. When UR in the expression 14 is a function for outputting a value which increases as a*b* increases in a red direction, the color gamut can be used sufficiently in the red direction. The same rule can also apply to the expression 15.
As described above, the technique disclosed in JP 2005-176280 A can solve the problems of the Kueppers Technique disclosed in U.S. Pat. No. 4,812,899 and the dividing technique disclosed in JP 2001-136401 A, so that colorants CMYKRGB can be generated continuously (without any discontinuous point) while calorimetric reproduction can be performed for the output device containing primary colors CMY and extra colors KRGB.
In the technique disclosed in JP 2005-176280 A, a great deal of time is however required for retrieving Kmax, Kmin, Rmax, Rmin, Gmax and Gmin. Generally, a model as given by the expressions 8 and 9 is often used for colorimetric reproduction. When, for example, the width of retrieval of K is 256 gradations, the expressions 8 and 9 must be repeated 256 times to calculate Kmin and Kmax. After K is fixed, the expressions 8 and 9 must be further repeated 256 times to retrieve Rmax and Rmin. After KR are fixed, the expressions 8 and 9 must be further repeated 256 times to retrieve Gmax and Gmin. That is, the solution of the expressions 8 and 9 must be repeated 256×3 times in total. It is to be understood that the number of times is enormous even in the case where a model easy in solution is used. When the model used is a nonlinear model such as a neural network model, a nonlinear optimizing method etc. is applied to the solution of the expression 9 but it is known that a great deal of processing time is required for the nonlinear optimizing method. It is also to be understood that the technique can hardly be used in practice in terms of processing time when extra colorants such as B are added to CMYKRG, because the number of times for retrieval must be increased in accordance with the addition of the extra colorants.
In the technique disclosed in JP 2005-176280 A, there is no consideration for the case where the total amount of coloring materials in the output device is limited. For example, assume that the limited total amount is 300% in the output device using six colorants CMYKRG. Assume that the dot area ratio of each color material of CMYKRG is in a range of from 0 to 100%. Assume that the total amount of CMYKRG calculated by the technique disclosed in JP 2005-176280 A is 350% (e.g. C=50%, M=50%, Y=50%, K=100%, R=50% and G=50%). On this occasion, a method for keeping the ratios of respective colorants simply to set the total amount of the colorants to 350% or a method for retrieving CMYKRG to minimize color differences may be conceived to set CMYKRG in the limited total amount. In the former method, color differences however increase so greatly that colorimetric color reproduction is spoiled. In the latter method, continuity of CMYKRG becomes an issue. Moreover, a greater deal of retrieval time is required for minimizing color differences within the limited total amount.
As a further technique for deciding extra colorants, for example, a method for converting RGB into YMCKRGB and adjusting colorants in accordance with functions with respect to lightness, chromaticness and hue while maximizing extra colorants with respect to a color of maximum chromaticness which can be reproduced in two of the three colors YMC has been disclosed in JP 2005-59361 A (corresponding to US 2005/0052670 A). Also in this technique, color continuity can be kept. Moreover, conversion of actually input RGB into YMCKRGB can be processed speedily because application of the functions is required merely.
For application of this technique, it is however necessary to set the functions appropriately. There is no way but the experimental way of deciding the functions because the functions cannot be set theoretically. For this reason, not only enormous processing is required for deciding the functions but also it is unknown whether the decided functions are optimal or not. This is due to the fact that seven parameters cannot be uniquely decided from three parameters as described above. In JP 2005-59361 A (corresponding to US 2005-0052670 A), there is a problem that extra colors cannot be uniquely decided because the number of functions allowed to be set is infinite, and extra colors vary in accordance with the setting of the functions.
A technique for deciding CMYKRGB from RGB by applying a simple function uniformly has been described in JP 2005-205812 A. Particularly, a technique for extending a color gamut by reducing the amounts of extra colors in a low-lightness portion to prevent lowering of chromaticness of the low-lightness portion when extra colors are used has been described in JP 2005-205812 A. In color conversion due to application of the simple function as described in JP 2005-205812 A, color consistency cannot be warranted so that it is very difficult to set the function for the same reason as in the technique described in JP 2005-59361 A (corresponding to US 2005/0052670 A) when color consistency is considered.
In the foregoing examples, all of the related art and limitations related thereto are intended to be illustrative and not exclusive. Other limitations of the related art will become apparent to those skilled in the art on a reading of the specification and a study of the drawings.